Crystal structure and complex magnetic properties of R11Pd4In9 compounds (R = Y, Gd–Er)

Abstract Magnetic properties of the R11Pd4In9 compounds (R = Y, Gd–Er) were investigated by means of X-ray diffraction and magnetic measurements. Three of these compounds, namely those with R = Y, Ho and Er, are newly synthesized. The compounds crystallize in the orthorhombic Nd11Pd4In9-type crystal structure (oC48, Cmmm) in which the rare earth atoms occupy five nonequivalent sublattices. Magnetic properties of the investigated compounds are related mainly to the R3+ ions, except the case of Y11Pd4In9 which is a Pauli paramagnet. For R = Gd-Er, the values of effective magnetic moments in the paramagnetic state are close to the free R3+ ion values while the moments in the ordered state at T = 2 K and H = 90 kOe are lower than the respective R3+ moments. The compounds have complex magnetic properties. All paramagnetic Curie temperatures are positive suggesting that the ferromagnetic interactions are predominant. However, the low temperature data indicate an antiferromagnetic order. With increase of temperature the magnetic properties change from antiferro-to ferrimagnetic and finally to paramagnetic ones. The critical temperatures of magnetic ordering do not fulfill the de Gennes scaling, indicating a crystalline electric field contribution to stabilization of the magnetic order at low temperatures. The neutron diffraction measurements, performed for Ho11Pd4In9, reveal a coexistence of two magnetic phases at low temperatures: the antiferromagnetic with propagation vector k = [0,0,½] and the ferrimagnetic one with k = [0,0,0]. The antiferromagnetic order is predominant at low temperatures while the ferrimagnetic one dominates at intermediate temperatures.


Introduction
The rare-earth-transition metal-In (R-T-In) ternary systems form a rich group of the intermetallic compounds with interesting crystal structure and unique physical properties [1]. In recent years the isostructural R 11 Ni 4 In 9 compounds (Nd 11 Pd 4 In 9 -type structure, Pearson symbol oC48, space group Cmmm) were intensively investigated. According to magnetic measurements they exhibit complex magnetic properties at low temperatures with multiple magnetic transitions [2][3][4][5][6]. Investigation of the fibrous samples of R 11 Ni 4 In 9 (R ¼ Gd, Tb, Dy and Ho) revealed strong magnetic anisotropy with easy magnetization along the c-axis [4][5][6]. Neutron diffraction data for R 11 Ni 4 In 9 (R ¼ Tb and Ho) showed that magnetic moments in different sublattices order at different temperatures [6].
During investigation of the R-Pd-In system at 870 K an existence of the R 11 Pd 4 In 9 (R ¼ La, Ce, Pr, Nd, Sm, Gd, Tb, Dy) compounds [7] with the Nd 11 Pd 4 In 9 -type structure [8] has been established. The compounds have complex crystal structure in which the rare earth atoms occupy five nonequivalent crystallographic positions.
Among the R 11 Pd 4 In 9 compounds, their magnetic properties have already been determined only for Ce 11 Pd 4 In 9 , which is a ferromagnet below T c ¼ 18.6 K with additional order-order magnetic transition at T t ¼ 1.6 K [9].
This work is a part of our investigation of magnetic properties of ternary rare-earth-transition metal indides, in purpose to determine the influence of different factors, like: composition, crystal structure and chemical bonding, on magnetic properties of these compounds. In the previous work we have concentrated on the compounds with T ¼ Ni [2,3,10]. In this work we report the results of X-ray diffraction and dc magnetic measurements of the R 11 Pd 4 In 9 (R ¼ Y, Gd-Er) compounds. From these data, the crystal structure parameters at room temperature as well as magnetic properties within the temperature range between 1.9  In order to explain the complex magnetic properties of Ho 11 Pd 4 In 9 , additional neutron diffraction measurements at low temperatures were performed.

Experiment
The samples of R 11 Pd 4 In 9 were prepared by arc-melting of high purity metals (99.9 wt% purity for R, 99.99 wt% for Pd and In) having total mass of 1.5 g under a pure argon atmosphere. The buttons were sealed in evacuated silica tubes and annealed at 870 K for one month. The Table 1 Crystallographic data obtained from Rietveld refinement, based on the X-ray powder diffraction patterns collected at room temperature for R 11 Pd 4 In 9 (Nd 11 Pd 4 In 9 -type structure, space group Cmmm).  and c along with the unit cell volume V for the R 11 T 4 In 9 (T ¼ Ni, Pd) compounds as a function of r(R 3þ ) -the effective ionic radius of heavy rare-earths with coordination number VI. The filled triangle symbols refer to the experimental data for R 11 Pd 4 In 9 as presented in this work while the open ones -to the literature data from Ref. [7]. The open circles refer to the R 11 Ni 4 In 9 series accordingly to the literature data from Refs. [2,3,5,10]. (b) Relative changes in the lattice parameters of R 11 T 4 In 9 (T ¼ Ni, Pd) as a function of r(R 3þ ). Δa ¼ [(a(Pd)-a(Ni))/a(Ni)] � 100%, etc. The radii were taken from Ref. [12].
powdered polycrystalline samples were measured at room temperature using a PANalytical X'Pert PRO diffractometer (Cu K α -radiation, Bragg-Brentano geometry, measured angle interval 2θ ¼ 10-130 � , step scan mode, step size in 2θ ¼ 0.026 � , 480 s/step). The FullProf [11] program package was used for X-ray phase and Rietveld analysis of the collected data set. The magnetic measurements were carried out using a vibrating sample magnetometer (VSM) option of the Quantum Design PPMS platform. Three types of magnetic measurements were performed: collecting ZFC (zero field cooling) and FC (field cooling) magnetic susceptibility curves in applied field of H ¼ 50 Oe from 1.9 to 390 K (in order to determine phase transition temperatures), then scanning from 1.9 K up to 390 K in magnetic field of 1 kOe (in order to determine the effective magnetic moment μ eff and paramagnetic Curie temperature θ p )

Table 2
Magnetic properties of R 11 Pd 4 In 9 (R ¼ Gd-Er): the Curie and transitions temperature (T c , T t ), the paramagnetic Curie temperature (θ p ), experimental (exp.) and theoretical (theor.) values of the effective magnetic moment (μ eff ) and of the moment in the ordered state (μ) at T ¼ 1.9 K (or 2.0 K for Tb 11  For the polycrystalline sample of Ho 11 Pd 4 In 9 additional powder neutron diffraction measurements with the use of the E6 diffractometer installed at the BERII reactor (BENSC, Helmholtz-Zentrum Berlin) were performed. The incident neutron wavelength was λ ¼ 2.432 Å while temperature ranged from 1.5 up to 24.6 K The Rietveld-type program FullProf [11] was used for processing the data.

Crystal structure
X-ray powder diffraction data collected at room temperature for the R 11 Pd 4 In 9 samples indicate ( Fig. 1 shows exemplary data for Ho 11 Pd 4 In 9 ) that the investigated compounds crystallize in the Nd 11 Pd 4 In 9type crystal structure (Pearson symbol oC48, space group Cmmm) [8]. Fig. 2 shows the projection of the atoms on the xy plane for Ho 11   [In3Pd 4 Ho 8 In 2 ]. The Ho atoms, which are situated at five different Wyckoff positions, occupy one layer of the structure (z ¼ 0) while the second one (z ¼ ½) is occupied by the palladium and indium atoms. Refined lattice parameters and atomic coordinates are presented in Table 1 and they are in good agreement with the previous results reported in Ref. [7]. The dependence of the lattice parameters a, b and c and the unit cell volume V (Fig. 3a) vs. effective ionic radius [12] is almost linear and agrees with the lanthanide contraction. The novel R 11 Pd 4 In 9 compounds with R ¼ Y, Ho and Er prolong the concerned series.

dc magnetic susceptibility
The results of magnetic measurements for the R 11 Pd 4 In 9 compounds (R ¼ Gd-Er) are presented in Fig. 4a-e and 5a-5f and summarized in Table 2. At high temperatures the reciprocal magnetic susceptibilities of all compounds obey the Curie-Weiss law. The paramagnetic Curie temperatures, as determined from these data, are positive, while the values of effective magnetic moments are close to those predicted for the free R 3þ ions (see Table 2).
With decrease of temperature a sharp increase of magnetic susceptibility is observed at 66, 106, 88, 18.7 and 19.6 K for R ¼ Gd, Tb, Dy, Ho and Er, respectively (see upper insets in Fig. 4a-e). The above temperatures have been determined from inflection points in the ZFC χ(T) curves taken at 50 Oe and are listed in Table 2 Table 2.
Deviations from the Curie-Weiss law are observed below 250 K (R ¼ Gd and Tb), 170 K (R ¼ Dy), 60 K (R ¼ Ho) and 40 K (R ¼ Er) indicating existence of short-range magnetic order above corresponding Curie temperatures.
Magnetic susceptibility of Y 11 Pd 4 In 9 (Fig. 6) takes small values (<0.001 emu/mol) over broad temperature range suggesting that Y 11 Pd 4 In 9 is a Pauli paramagnet. This result is in agreement with small magnetic moment (2.5•10 À 3 μ B /Y atom) determined from magnetization measured at 1.9 K. The increase of susceptibility below 100 K is probably related to small amount of magnetic atoms present as impurity in yttrium which is of 99.9 wt% purity.

Magnetization
Magnetization curves and hysteresis loops for R 11 Pd 4 In 9 (R ¼ Gd-Er), measured at selected temperatures in external magnetic fields up to 90 kOe (9 T), are presented in    It is worth noting that hysteresis loops collected at the lowest temperatures for R 11 Pd 4 In 9 (R ¼ Tb and Dy) show a number of jumps indicating field-induced switching between metastable magnetic orderings.
Different shape of magnetization vs. external magnetic field curves is observed in R 11 Pd 4 In 9 (R ¼ Ho, Er). In the ordered state, regardless the temperature, these dependences are similar to those observed for ferrimagnetic materials. The critical fields of metamagnetic transitions are low, namely, they equal to 5.6 kOe (1. It is worth noting that none of the magnetization curves shows saturation at 90 kOe and the determined magnetic moments per rare earth atoms are smaller than the theoretical values expected for free R 3þ ions, even at the lowest temperatures.
The values of critical and coercivity fields, as determined from the magnetization vs. applied magnetic field dependences, are summarized in Table 3.

Neutron diffraction data
The results of powder neutron diffraction data for Ho 11 Pd 4 In 9 , collected at three selected temperatures (1.5, 11.7 and 24.6 K), are presented in Fig. 7. Analysis of the paramagnetic pattern taken at T ¼ 24.6 K confirms the crystal structure of the Nd 11 Pd 4 In 9 -type (R Bragg ¼ 6.51%, R F ¼ 4.71%). Additional Bragg reflections of magnetic origin are

Table 4
Ho magnetic moments as refined from the neutron diffraction pattern of Ho 11 Pd 4 In 9 collected at 1.5 K together with corresponding reliability factors. The AFM and FiM denote the antiferro-and ferrimagnetic contributions to the magnetic structure, respectively. Analysis of the diffraction pattern at 1.5 K shows that the most intense reflections correspond to the antiferromagnetic structure with magnetic unit cell doubled along the c-axis when compared to the crystallographic one (k ¼ [0,0,½]). The best fit has been obtained for a magnetic structure with all holmium magnetic moments within the crystallographic unit cell coupled ferromagnetically and parallel to the c-axis direction while the moments in the neighbouring cells along the caxis point at opposite direction (see Fig. 9a). The exact values of magnetic moments are listed in Table 4, where Ho1, …, Ho5 refer to atoms located at different Wyckoff sites as specified in Table 1. The holmium moments are significantly smaller than 10 μ B expected for a free Ho 3þ ion.
The small intensity reflections form a second group corresponding to a ferrimagnetic structure with partial compensation of magnetic moments (see Fig. 9b). The magnetic unit cell is identical to the crystallographic one (k ¼ [0,0,0]). The holmium magnetic moments within each Wyckoff site are coupled ferrimagnetically, namely:  Table 4.
Thermal evolution of the diffraction pattern indicate that two contributions to the magnetic structure, the antiferro-(AFM) (k ¼ [0,0,½]) and ferrimagnetic (FiM) (k ¼ [0,0,0]) ones, have different temperature dependence. Fig. 8 shows the intensity vs. temperature plot for selected Bragg reflections taken as representatives of the antiferro-and ferrimagnetic contributions to the magnetic structure together with those related to the crystal structure. Due to reflection overlapping the respective sums of intensities are shown as indicated in the Fig. 8 legend.
Intensities of the AFM-related reflections decrease monotonically with temperature and are found absent in the pattern taken at 11.7 K. The highest rate of decrease is found between 4.2 K and 9.7 K. The intensities of the FiM-related reflections show different behavior, they undergo a rapid increase in the temperature range from 4.2 K to 9.7 K, then remain almost constant up to 11.7 K and finally gradually decrease and reach zero in the vicinity of 20 K.
Presented data indicate a coexistence of the antiferro-and ferrimagnetic orderings within the majority of temperature range of the

Table 5
Interatomic distances (δ) and coordination numbers (CN) in the Ho 11 Pd 4 In 9 compound, accordingly to the crystallographic data of Ho 11 Pd 4 In 9 presented in Table 1. Standard deviations are smaller than 0.006 Å. All distances within the first coordination spheres are listed.   11. The Curie temperatures (T c ) and paramagnetic Curie temperatures (θ p ) vs. de Gennes factor for R 11 T 4 In 9 (R ¼ Gd-Er). The data for T ¼ Ni are taken after Refs. [2,3] while for T ¼ Pd are reported in this work. The straight lines indicate theoretical dependence, predicted by the RKKY theory, with Gd-based compounds taken as reference (see main text for details). magnetically ordered state. The antiferromagnetic order is predominant at low temperatures while the ferrimagnetic one dominates at intermediate temperatures. Both magnetic phases disappear in the vicinity of the Curie temperature. The thermal evolution of different contributions to the magnetic structure is in agreement with the complex temperature dependence of magnetic susceptibility at low temperatures (see the inset in Fig. 4d).

Discussion
The work reports the results of X-ray and neutron powder diffraction and dc magnetic measurements for the R 11 Pd 4 In 9 (R ¼ Y, Gd-Er) series of compounds. The X-ray diffraction data confirm the orthorhombic crystal structure of the Nd 11 Pd 4 In 9 -type which was originally determined, using single-crystal X-ray diffractometry, for Nd 11 Pd 4 In 9 [8] and Gd 11 Ni 4 In 9 [4] and described in detail in Refs. [4,5,7,8,10]. The main determined structural features of the compounds are as follows: 1) the structure consists of two layers alternating along the shortest c-axis (much shorter than both the a-or b-axis), thus the layer of larger R atoms forms nets of tetragons and triangles at z ¼ 0, while the layer of smaller in size (Ni,Pd)/In atoms forms nets of tetragons and pentagons at z ¼ ½; 2) the crystal structure is formed by the AlB 2 (RNi 2 ) and CsCl (RIn)-type fragments; 3) the lattice parameters decrease linearly with decreasing effective ionic radius of rare earth (Fig. 3a) due to the lanthanide contraction; 4) polycrystalline samples of the compounds are built from well-defined fibers (or rods) quickly growing along the short c-axis due to the presence of short In-In chemical bonds in the a-b plane. The anisotropy of the crystal structure corresponds with strong anisotropy of the physical properties [5].
The refined lattice parameters and atomic coordinates, presented in Table 1, are in good agreement with the previous results for polycrystalline samples reported in Refs. [7] as well as with the single-crystal data for Gd 11 Ni 4 In 9 [4]. The lattice parameters of the R 11 Pd 4 In 9 compounds are only little larger than those for the isostructural R 11 Ni 4 In 9 intermetallics (see Fig. 3b) leading to similar magnetic properties in these two series of compounds. It is worth noting that the relative changes in the a and b lattice parameters (Δa ¼ [(a(Pd)-a(Ni))/a(Ni)] � 100%, etc.), and accordingly the unit cell volume V, increase with decreasing effective ionic radius of the rare-earth element while the change in the shortest c-parameter rather decreases indicating a significant role of the transition element in the interatomic bonding. The refined interatomic distances and coordination numbers of atoms in Ho 11 Pd 4 In 9 , listed in Table 5, well agree with the single-crystal data for Gd 11 Ni 4 In 9 [4].
The work reports the interesting magnetic properties of the R 11 Pd 4 In 9 compounds (R ¼ Y, Gd-Er). Y 11 Pd 4 In 9 is a Pauli paramagnet while the other compounds (R ¼ Gd-Er) order magnetically at low temperatures. The results of the macroscopic magnetic measurements are summarized in Table 2. The effective magnetic moments determined from high temperature data in the paramagnetic state are very close to the free R 3þ ion values confirming that magnetic moments in R 11 Pd 4 In 9 (R ¼ Gd-Er) are localized solely on the rare earth R 3þ ions. The determined values of the paramagnetic Curie temperatures (θ p ) are positive indicating predominantly ferromagnetic character of the magnetic interactions. Noticeable deviations of the inverse magnetic susceptibility from the Curie-Weiss behavior, visible above respective Curie temperatures, are characteristic of short-range magnetic order. Temperature dependence of the magnetic susceptibilities (see the upper insets in Fig. 4a-e) and magnetization curves (see Fig. 5a-f) indicate a change of magnetic order from the antiferromagnetic ground state at low temperatures, through ferrimagnetic at intermediate temperatures and finally to paramagnetic state. The critical temperatures of magnetic ordering (T c ) are larger than the corresponding paramagnetic Curie temperatures (θ p ), indicating a presence of an antiferromagnetic contribution to the predominant ferromagnetic interactions, as expected for the high-temperature ferrimagnetic (FiM) phase. The critical and coercivity fields, determined from the magnetization curves and hysteresis loops, show a significant increase while comparing those of Gd 11 Pd 4 In 9 (L ¼ 0, purely S state) and Tb 11 Pd 4 In 9 (L > 0), confirming the influence of crystalline electric field on magnetic properties. Further increase of the number of 4f electrons of the rare earth element leads to decrease of both the critical and coercivity fields.
The results of neutron diffraction experiment for Ho 11 Pd 4 In 9 show a presence of the complex temperature dependent magnetic structure at low temperatures. The holmium magnetic moments occupying five different Wyckoff sites are of different magnitudes (or are zero in the case of Ho5 in the FiM structure). The moments are parallel or antiparallel to the c-axis with exception for Ho1 in the FiM phase, whose moments are inclined at an angle of about 40 � to the c-axis. Such a complex magnetic structure results from the complex crystal structure in which the rare earth atoms R occupy five nonequivalent sites with the similar R-R nearest neighbour interatomic distances within particular site or between the sites. The different rare earth sites are characterized by different local site symmetry, namely: m for the 8p site, m2m for the 4i sites, 2mm for the 4g site and mmm for the 2a site. Therefore, the magnetic structure results from competition between exchange interactions and local crystalline electric field.
The most of the Ho magnetic moments in the determined magnetic structures of Ho 11 Pd 4 In 9 (AFM and FiM) are parallel to the c-axis. This result is in agreement with the data for R 11 Ni 4 In 9 (R ¼ Tb, Dy) where the c-axis was found to be an easy magnetization direction [5]. The magnetic structures in the isostructural R 11 Ni 4 In 9 (R ¼ Tb, Ho) are complex with a number of temperature induced magnetic transitions and magnetic moments pointing at different directions [6], however, those structures are not the same as the ones reported here for Ho 11 Pd 4 In 9 .
One can expect that such a scenario with a number of temperatureor field-induced magnetic transitions appearing consecutively is probably also realized in other members of the investigated R 11 Pd 4 In 9 (R ¼ Gd-Er) family of compounds, whose magnetic structures have not yet been resolved. Fig. 10 shows the distributions of the Ho atoms located at different sites. The shortest Ho-Ho distances are marked. In the majority of cases these distances are larger than the sum of atomic radii equal to 3.54 Å. Such a large R-R interatomic distances, found in both series of the R 11 T 4 In 9 (R ¼ Ni, Pd) isostructural compounds, suggest that the magnetic interactions between the rare earth magnetic moments are predominantly driven by the indirect exchange interactions of the RKKYtype [13]. Fig. 11 shows the experimentally determined Curie temperatures and paramagnetic Curie temperatures plotted against the de Gennes factor. The straight lines indicate theoretical dependence, predicted by the RKKY theory, with Gd-based compounds taken as reference owing to the fact that the Gd 3þ ion is in the S-state with zero orbital momentum and thus is not influenced by the crystalline electric field. The observed large discrepancy between the experimental and calculated temperatures, especially visible in T C for R ¼ Tb and Dy, indicates strong influence of the crystalline electric field (CEF) on stability of the magnetic order in both series of compounds [14]. Similar discrepancies, attributed to the influence of CEF, have been observed in RRh 4 B 4 [15] and R 2 CoGa 8 (R ¼ rare earth element) [16].
Comparison of the magnetic data for both series of the isostructural R 11 T 4 In 9 (T ¼ Ni, Pd) compounds indicates limited influence of the transition element T: Ni (3d) and Pd (4d). For both the series the magnetic moments are localized solely on the rare earth atoms. The Ni and Pd atoms do not possess localized magnetic moments. The compounds with R ¼ Gd, Tb, Dy and T ¼ Ni, Pd as well as two members of the Pdseries, namely, R 11 Pd 4 In 9 (R ¼ Ho, Er), show similar magnetic properties at low temperatures. With increase of temperature the antiferromagnetic ground state transforms in to the ferrimagnetic structure at T t which finally undergoes a transition to the paramegnetic state at T c . The transition temperatures T t and T c are similar in both the series (see Table 1 in Ref. [3] and Table 2 in this work). Ho 11 Ni 4 In 9 is an exception as it is found purely antiferromagnetic while Er 11 Ni 4 In 9 is non-existent.

Summary
The R 11 Pd 4 In 9 compounds (R ¼ Gd-Er) with the complex crystal structure in which the rare earth atoms occupy five nonequivalent sites present interesting magnetic properties. The magnetic moments, localized solely on the rare earth atoms, show complex magnetic ordering with the antiferromagnetic ground state at low temperatures. Applying temperature or external magnetic field induces a transition to the ferrimagnetic order. The critical temperature of magnetic order T c , particularly those for R ¼ Tb and Dy, do not obey the de Gennes relation indicating an influence of the crystalline electric field. The powder neutron diffraction data for Ho 11

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.